Finite Group DatabasebetaFinite Group Databasebeta| order | 21450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C5 |
| direct product | C13×C11⋊((C5⋊D5)⋊C3) |
| unambiguous semidirect product | C11⋊(C13×(C5⋊D5)⋊C3) |
| unambiguous semidirect product | (C5⋊D55)⋊(C3×C13) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | C11⋊((C5⋊D5)⋊C3) |
| commutator, cosocle, hypocenter | C52×C11 | C2×C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C52×C11×C13 | C2×C3 |
| LCS | G ▷ C52×C11 | |
| UCS | C1 ◁ C13 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2145 |
845 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21450, 75);